document.write( "Question 638941: How many pounds of candy worth 50 cents a pound must be mixed with how many pounds of more expensive candy worth 90 cents a pound to create a 75-pound mixture worth 76 cents a pound? \n" ); document.write( "

Algebra.Com's Answer #402493 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = pounds of 50 cents/pound candy needed
\n" ); document.write( "Let $\"+b+\"$ = pounds of 90 cents/pound candy needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+75+\"$
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.9b+%29+%2F+75+=+.76++\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(2) $\"+.5a+%2B+.9b+=+75%2A.76+\"$
\n" ); document.write( "(2) $\"+.5a+%2B+.9b+=+57+\"$
\n" ); document.write( "(2) $\"+5a+%2B+9b+=+570+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+5+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+9b+=+570+\"$
\n" ); document.write( "(1) $\"+-5a+-+5b+=+-375+\"$
\n" ); document.write( " $\"+4b+=+195+\"$
\n" ); document.write( " $\"+b+=+48.75+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+75+\"$
\n" ); document.write( "(1) $\"+a+%2B+48.75+=+75+\"$
\n" ); document.write( "(1) $\"+a+=+26.25+\"$
\n" ); document.write( "26.25 pounds of 50 cents/pound candy are needed
\n" ); document.write( "48.75 pounds of 90 cents/pound candy are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.5a+%2B+.9b+%29+%2F+75+=+.76++\"$
\n" ); document.write( "(2) $\"+%28+.5%2A26.25+%2B+.9%2A48.75+%29+%2F+75+=+.76++\"$
\n" ); document.write( "(2) $\"+%28+13.125+%2B+43.875+%29+%2F+75+=+.76++\"$
\n" ); document.write( "(2) $\"+57%2F75+=+.76+\"$
\n" ); document.write( "(2) $\"+57+=+.76%2A75+\"$
\n" ); document.write( "(2) $\"+57+=+57+\"$
\n" ); document.write( "OK \n" ); document.write( "

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